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$ \def\bra#1{{\langle#1|}} \def\ket#1{{|#1\rangle}} $ The mathematical notation and the respective circuits (without swaps) for little- and big-endian of the $QFT$ are shown below: Little-endian: $$QFT_N(\ket{x_1x_2\dots x_n}) = \frac{1}{\sqrt{N}}(\ket{0}+e^{2\pi i[0.x_n]}\ket{1})\otimes(\ket{0}+e^{2\pi i[0.x_{n-1}x_n]}\ket{1})\otimes\dots\otimes(\ket{0}+e^{...


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